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A general approach based on mid-infrared (MIR) laser scanning is proposed to measure the 3-D ice shape no matter whether the ice is composed of clear ice, rime ice, mixed ice, or even supercooled water droplets or films. This is possible because MIR radiation penetrates ice and water only within a depth of less than 10 micrometers. First, an MIR laser point scanning technique is implemented and verified on transparent glass and clear ice. Then, to improve efficiency, an MIR laser line scanning method is developed and validated on different models. At last, several sequential MIR laser line scans are applied to trace the 3-D shape evolution of the continuous ice accretion on an airfoil in an icing wind tunnel. The ice growth process can be well observed in the results. The MIR scan shows a good agreement with the traditional visible laser scan on a plastic replication of the final ice shape made by the mold and casting method.
© 2015 Optical Society of America
1. Introduction
The ice accretion is always a severe threat to the safe flight of aircrafts. It is well known that the aerodynamic performance of aircrafts deteriorates tremendously mainly because accreted ice changes the optimal aerodynamic shape of wings [1]. Therefore, accurate and efficient measurements of ice shapes are crucial for not only icing experiments and aircraft certification but also for numerical simulations that predict how ice grows. Most icing experiments are carried out in icing wind tunnels, which is more economical and controllable than flight experiments.
Ice shape measurement techniques can be categorized into contact measurement methods and non-contact methods. The former includes the hand tracing method and the mold and casting method [2]. The unavoidable problem with contact measurement techniques is that measurements interrupt the icing process; therefore, they can only be done once at the end of the experiments. Worse more, some fragile ice features may get damaged during the measurements. Existing non-contact methods are photogrammetry [3], microwave or ultrasonic transducers [4], and laser scanning [5]. Microwave or ultrasonic transducers can only measure the thickness of several points where the thickness is an average value in the vicinity of the transducer. The accuracy of photogrammetry and laser scanning is totally dependent upon the surface light reflectivity of ice. Ice grown on the surface of aircrafts is classified into rime ice and clear ice, according to whether supercooled water that impacts the surface freezes instantly or not. The mixed ice of these two types is also common. For rime ice, the surface reflectivity is usually high enough but special attention should be given to the sub-surface scattering in most cases. The problem is much more severe for clear ice which is always translucent or even transparent. This is why many ice shape measurements only confine to rime ice; otherwise some opaque powder or spray (based on titanium dioxide) has to be applied on the ice surface to increase reflectivity [6,7]. In this case, the so called “non-contact” methods are no different from the contact methods, because the icing process is chemically interrupted by the opaque spray as well.
With the development of computer vision technology, the high accuracy, great robustness, and decreasing cost, commercial 3-D laser scanners are popular in many fields, such as industrial inspection, cultural heritage digital archiving, and reverse engineering. The ice shape measurement in icing wind tunnels is no exception. More and more recent researches have demonstrated that laser scanning can document details of different ice shapes. For example, ice horn, ice roughness, runback-spanwise ridges, and even ice scallop have all been measured by laser scanning [8–11]. The efficiency and accuracy of laser scanning is proved high enough to replace the traditional mold and casting method. However, as mentioned before, all these laser scanning measurements have bypassed the optical challenge of ice by painting the ice surface with opaque spray, which significantly intervenes in ice growth and consequentially impedes continuous observation of the whole icing process. In the computer vision community, there are also lots of interests studying how to reconstruct 3-D shapes of transparent or translucent objects [12]. But those methods are usually still case studies and therefore only applicable to very specific objects, not to mention complicated ice shapes. Moreover, a method can only be practical when it is able to measure the 3-D shape of rime ice, clear ice and mixed ice without any difference. It should be noted that sometimes the ice surface may be covered with a supercooled water film, which makes the shape measurement even more challenging.
The innovation of this paper is to introduce an MIR laser scanning technique to measure the shape of any ice type. For such a technique, as will be discussed in the following, no spraying or any other procedure is required to prepare the ice surface. Accordingly, the scanning measurement can be operated at any time during the icing process and this method treats rime ice, clear ice, mixed ice, or even water films the same. In this case, the 3-D shape evolution of the continuous ice growth on the aircrafts’ surface can be measured with high efficiency and accuracy. The basic idea behind this technique is that an IR camera documents the radiative pattern rather than the reflected pattern after an object is scanned (also heated) by a moving MIR laser pattern. This idea can be traced back to the application of thermographic nondestructive testing [13], where radiative patterns after uniform heating revealed the subsurface structure of defects in materials. Pioneering work, based on a similar idea, extracted orientation and depth information of an object that was exposed to a diffuse heating device to reconstruct some simple shapes (planes and cylinders) [14]. However, there have been no further applications of this “Shape from uniform heating” on complicated shapes. Eren et al. first proposed to use MIR laser point scanning to measure 3-D shapes of transparent objects such as glass and plastics [15]. Their method was later improved by projecting an MIR laser line onto translating glass [16]. Their method was also adapted to measure the geometry of metals with specular surfaces, in which the MIR laser was replaced by a near infrared laser to ensure a high absorption coefficient for specific metals [17–19]. This paper improves their idea and applies MIR laser scanning to ice shape measurements.
2. Radiative properties of ice
For a semitransparent medium, such as ice, water or glass, the radiation incident on a surface may be absorbed, reflected, and transmitted. Relations among these components can be described by the following radiation balance [20]:
With definitions of a spectral, hemispherical absorptivity 𝑎𝜆 = 𝐺𝜆, 𝑎/𝐺𝜆, reflectivity 𝑟𝜆 = 𝐺𝜆, 𝑟/𝐺𝜆, and transmissivity 𝑡𝜆 = 𝐺𝜆, 𝑡/𝐺𝜆, respectively, Eq. (1) can be rewritten as:Both Eq. (1) and Eq. (2) are simply representations of conservation of energy. For a blackbody, it absorbs all incident radiation regardless of wavelength, so it follows that 𝑎𝜆 = 1, 𝑟𝜆 = 0, 𝑡𝜆 = 0. At the same time, the blackbody is a diffuse emitter, that is, it emits radiation independent of direction.The fundamental hypothesis of a visible light laser scanning technique is that the observed object has an opaque and diffuse surface, so that reflected light observed by the camera represents the direct illumination by the light source. For an MIR laser scanning technique, the fundamental hypothesis and principle remain unchanged, but the diffuse surface means a diffuse emitter rather than a diffuse reflector because re-emitted radiation, resulting from MIR laser excitation, is observed. Therefore, it would be ideal if the observed object interacts with incident radiation like a blackbody. In the visible light range, clear ice is not similar to a blackbody at all. But the reflectivity, transmissivity, and absorptivity of any material changes according to the incident radiation wavelength, so it is possible that at a certain spectral range clear ice functions like a blackbody. The reflectivity of clear ice is as shown in Fig. 1(a). Because clear ice, rime ice, and water usually co-exist in wind tunnel experiments, we also show the reflectivity of water and snow with varied granular size (similar to rime ice) in Fig. 1(a). In the whole documented spectrum (0~15 μm), both clear ice and water display very low reflectivity (<10%), while three different snow samples with varied granular size show high reflectivity (>95%) in the visible light range and show low reflectivity (<10%) in the infrared light range. This demonstrates again that the traditional light-reflection-based laser scanning may work for rime ice rather than clear ice. The transmissivity can be represented by the penetration depth (i.e. the depth at which the intensity has decreased to 1/𝑒. Here, 𝑒 is the Euler’s number.). The penetration depth can be directly calculated from optical constants of the medium. In Fig. 1(b) we only show the penetration depth of light in clear ice and water, because it is well known that infrared light almost does not penetrate through rime ice [21]. It is noted that both curves are similar. The penetration depth of visible light in clear ice and water is more than 1 m, while that value drops tremendously in the infrared light range, less than 1 mm for 𝜆>2 μm. In this paper, a CO2 laser (𝜆 = 10.6 μm) was used as an MIR laser source. At 10.6 μm, the reflectivity of clear ice, rime ice, and water is less than 1% (see Fig. 1(a)) and the penetration depth of radiation in them is only around 7 μm (see Fig. 1(b)). In conclusion, both ice and water are almost opaque and absorb nearly all incident radiation at 10.6 μm, that is, 𝑎𝜆≈1, 𝑟𝜆≈0, 𝑡𝜆≈0.
To check whether ice is approximately a diffuse emitter, the spectral, directional emissivity of the ice surface is shown in Fig. 2(a). The spectral, directional emissivity 𝜀𝜆, 𝜃 (𝜆, 𝜃, 𝜑, 𝑇) of a surface is defined as the ratio of the intensity of the radiation emitted at the wavelength λ and in the direction of 𝜃 and 𝜑 to the radiation emitted by a blackbody at the same temperature 𝑇 and wavelength 𝜆. The theoretical curve in Fig. 2(a) can be estimated by the equation [25]:
here 𝑛 is the refractive index. For ice and water, 𝑛 does not change much in infrared light range. In the 8~14 μm range, 𝑛 of ice changes between 1.09 and 1.56, and 𝑛 of water changes between 1.11 and 1.29. We set an average value in the 8~14 μm range for ice 𝑛 = 1.28 and for water 𝑛 = 1.21. That is because experimental data of spectral, directional emissivity of ice, snow [26], and water [27] is also an average value in this spectral range. The experimental data and theoretical estimations of emissivity of ice and water show a good agreement. The spectral, directional emissivity of clear ice and water remain constantly high (𝜀𝜆, 𝜃>0.9) for modest exitance angle (𝜃<65°). For rime ice, its spectral, directional emissivity is even higher (𝜀𝜆, 𝜃>0.95 if 𝜃<75°). Despite the fact that the directional emissivity drops as the exitance ray approaches the tangential direction of the surface, both ice and water can be approximated as a diffuse emitter.
Fig. 2 (a) Directional emissivity of ice and water. (b) Spectral absorption, reflection, transmission, and emission associated with ice under the MIR laser radiation.
To summarize this section, an illustration about how ice interacts with the radiation of an MIR (𝜆 = 10.6 μm) laser is shown in Fig. 2(b). The ice surface absorbs nearly all the MIR laser radiation and a majority of absorbed radiation is re-emitted almost independent on view angles, which means the IR camera will “see” where the MIR laser ray hits. In addition, the foregoing discussion of radiative properties of ice and water has proved that the co-existence of varied ice types or water does not make any difference to the usage of MIR laser scanning. All these conclusions will lay the solid foundation for the coming MIR laser scanning method in next sections.
3. MIR laser point scanning
The applicability of MIR laser scanning on ice shape measurements was first verified by a point scanning method. The experimental setup is shown in Fig. 3(a). A Synrad’s 30 W continuous wave CO2 laser at 10.6 μm was used as the MIR laser source. Thermal images were recorded by an InfraTec’s ImageIR® 8300 IR camera whose sensibility spectral range is 2~5 μm and full frame resolution is 512 × 640 pixel. To protect the camera sensor from damage caused by direct intense laser radiation, a sapphire window was placed in front of the camera lens. The sapphire window is opaque at wavelengths higher than 8 μm and transparent between 2~5 μm. Positions of the CO2 laser and the IR camera were fixed, while the measuring object was moved by a XY positioning system. The positioning device, with an accuracy of 10 µm in both axes, can be programmable controlled to move from one location to another at a defined speed. For shape measurements, the MIR laser beam was raster scanned across the surface of the objects and the scanning of the positioning system was synchronized with the imaging of the camera. Before the measurements, some tests were done to identify a proper combination of scanning speed and laser power, so the temperature of the heating surface was increased not too much (less than 4 °C) while still detectable to the IR camera sensor. This is especially crucial for ice shape measurements, because too much heating will melt the ice. The laser power, the scanning speed, and the image frequency were set to 1 W, 20 mm/s, and 8 Hz, respectively. As the laser beam scans across the surface, a bright line pattern with an increasing intensity along the scanning direction should be observed in the IR camera. The intensity peak is located at the center of laser radiation. Two examples of thermal images of the scanning MIR laser beam on surfaces of glass and ice are shown in Fig. 3(b) and 3(c). The intensity peaks in both images are marked out with black dots, which were estimated by first finding the highest intensity in the whole image, and then computing the intensity-weighted centroid in a local small window.
Fig. 3 (a) Experimental setup for MIR laser point scanning. (b) Laser beam on glass. (c) Laser beam on ice. (d) Triangulation.
Triangulations are necessary to reconstruct 3-D shapes of the object from 2-D images recorded by the IR camera. Although the specific triangulation method varies according to different camera-laser setups [28], the core of all methods uses triangulations to recover the corresponding points in the real word space from pixels in image planes based on the pinhole camera model. The triangulation method used in this paper, follows the work of Marzani et al. [29], and is shown in Fig. 3(d). 𝛧0 is the initial reference point on the heated surface and its corresponding pixel in the image plane is 𝑑0. 𝛧1 is any heated point measured afterwards and 𝑑1 is its projected pixel. Following the projection geometry in Fig. 3(d), the height variation 𝛥𝛧 from 𝛧0 to 𝛧1 is
where 𝐶 represents the distance from the optical center to the laser beam. Also, the distance 𝛥𝑑 between 𝑑0 and 𝑑1 iswhere 𝑓 is the focal length. After some triangulations [29], 𝛥𝛧 is related to 𝛥𝑑 byBecause 𝐶, 𝑓, 𝜑, and 𝜃0 are constant values for a given camera-laser setup, we havewhere 𝛼, 𝛽, and 𝛾 are constants that can be determined by a calibration that measures at least three points whose positions are precisely known. It should be noted that an extra parameter β is used in Eq. (7) to correct some small errors due to the acquisition [29]. In this paper, the calibration was carried out by calculating height variations of laser heated points on a vertically translated glass sheet which was moved at a step of 5 mm and 50 mm in total.3.1 Point scanning on glass bowl and ice bowl
Because early publications [15,16] have already proven that MIR laser scanning is capable of measuring the shape of glass, our MIR laser point scanning technique was first validated on a transparent glass bowl. Then, the same technique was validated on an ice bowl. The ice bowl was made by filling water in the glass bowl and storing them in a freezer. It should be noted that the ice bowl is actually a negative mold of the glass bowl, so the ice bowl and the inner surface of the glass bowl share the same surface geometry. The glass bowl was later sprayed with white opaque powder, and then scanned by a traditional visible laser line scanning method. The scanning results of this painted glass bowl serves as the true data. The transparent glass bowl, the painted glass bowl, and the translucent ice bowl are shown in Fig. 4(a)-4(c), respectively. It is noted that subsurface structures within the ice bowl are also visible. The painted glass bowl was scanned twice at two different viewing positions. Then, a water-tight surface of the painted glass bowl was generated from two aligned point clouds by the Poisson surface reconstruction [30]. It is noted that the measured surface of the painted glass bowl suffers from some small error that may result from not enough painting (see Fig. 5(a) and 5(b)). However, it is enough to evaluate the MIR laser scanned results.
Fig. 5 Comparison of MIR laser point scanning on glass bowl and ice bowl. (a) Glass bowl point cloud and error. (b) Ice bowl point cloud and error. (c) Error distribution of glass bowl results. (d) Error distribution of ice bowl results.
Measured point clouds of MIR point scanning on the glass bowl and the ice bowl were compared with the reconstructed surface of the painted glass bowl. Results are shown in Fig. 5(a) and 5(b). The error is calculated in terms of the signed distance which is the closest Euclidean distance from the compared point to the reference surface. The distance has a negative value if the point lies inside the surface, and vice versa.
Measured point clouds of MIR point scanning on the glass bowl and the ice bowl were compared with the reconstructed surface of the painted glass bowl. Results are shown in Fig. 5(a) and 5(b). The error is calculated in terms of the signed distance which is the closest Euclidean distance from the compared point to the reference surface. The distance has a negative value if the point lies inside the surface, and vice versa.
Both point clouds show good agreements with the water-tight surface, especially at the bowl bottom where it is flat. Relatively larger deviations appear on the curved surface, which is also reported in [15]. One possible cause may be that a higher moving speed and a larger incident area of the MIR laser beam on a curved surface pose a challenge to estimate the radiation center through detecting the intensity peak. The ice bowl result displays smaller maximum deviation than the glass bowl result, which can also be demonstrated by the error distribution in Fig. 5(c) and 5(d). The mean signed distance and the standard deviation of the ice bowl result are −0.003 mm and 0.33 mm, while these two values of the glass bowl are −0.0078 mm and 0.50 mm, respectively. Again, this shows that our MIR laser point scanning method works better for ice than glass in terms of both accuracy and uncertainty. This difference between ice and glass may result from either a lower absorptivity or a less diffuse emission of the glass bowl.
In conclusion, the MIR laser point scanning method presented here is able to be applied to ice shape measurements. However, as discussed before, the point scanning method deteriorates when it comes to a complicated surface topography. Moreover, the most significant disadvantage of this method is that it is time consuming and results are always too sparse. In contrast, a line scanning method generates a considerably denser point cloud within much shorter time duration, and shall be discussed in the following section.
4. MIR laser line scanning
The laser line scanning method, a natural extension and a powerful alternative of the point scanning method [31], has emerged as early as in the 1980s. But almost all these methods are based on observing the diffuse reflection on a surface, so the light source is limited to either the visible light or the near infrared (NIR) light. The extension of the line scanning method to an MIR light source, based upon observing the diffuse emission on a surface, occurred only recently [16]. For a line scanning method, instead of raster scanning a single laser spot, a laser sheet is first created through proper lenses, then, projected onto the scene, and finally scanned across the surface of an object. The deformed laser line or strip on the object’s surface, observed by a camera, is a function of range or scene depth which can be estimated by intersecting laser sheet planes with corresponding optical rays passing through the deformed line and the optical center of the camera.
The MIR laser line scanning method presented in this paper is adapted from a visible laser line scanning method [32]. The scanning laser line is implemented by projecting a laser sheet on a rotating mirror mounted on the top of a galvo scanner. The experimental setup is intentionally kept almost the same as used for visible line scanning except that an IR camera, an MIR laser, and MIR optics are used here; see Fig. 6(a). Therefore, the visible line scanning method can be extended here with minimal software and hardware modifications. Also, the similar setup offers the possibility in future when the visible and MIR scanning methods will be applied simultaneously for purpose of a comparison or a complementation.
Fig. 6 (a) Geometrical description of MIR line scanning. (b) Checkerboard made from a PCB plate. (c) Checkerboard observed by an IR camera. (d) Printed black fiducial markers on a piece of white paper. (e) Fiducial markers observed by an IR camera.
The primary challenge for an MIR laser line scanning method lies in two aspects. The first is how to perform the geometric calibration for an IR camera. Traditional calibration methods for visual cameras will not work well for an IR camera which is sensitive to thermal radiation. For example, a very popular way is to print the checkerboard pattern on a piece of paper. Because of the even thermal distribution, the corner features of this pattern often look blurry to an IR camera even when a heat lamp is applied [33]. Many custom made calibration methods for thermal imaging have been proposed [34–37], the essential idea is to create a high radiation contrast pattern results from either a high temperature difference or a high emissivity difference. To keep consistent with our existing visible laser scanning method, a checkerboard pattern is still used for the IR camera calibration. But instead of printing this pattern on a piece of paper, it is made by etching away unwanted copper on a printed circuit board (PCB) [38]; see Fig. 6(b). Because of the low emissivity of copper and the high emissivity of the base material, a high contrast pattern is captured by the IR camera where copper appears black while the base material appears bright; see Fig. 6(c). In experiments, the PCB plate was placed in several positions, and then the recorded thermal images of the checkerboard pattern were processed by using Bouguet’s calibration toolbox [39] based on the method proposed by Zhang [40]. This geometric calibration method is widely used in the computer vision community for its ease, robustness, and high accuracy.
The second challenge is how to perform a geometric calibration for MIR laser planes. This calibration determines the position of each laser plane in the world coordinate system. Again, traditional laser calibration methods will not work directly for an MIR laser. For example, to calibrate an IR camera-laser system by a traditional method based on the concept of a complete quadrangle [41], the complete quadrangle has to be manufactured from glass instead of some material with a diffuse reflecting surface [16]. In our work, the MIR laser plane position was calibrated by scanning the laser sheet across two perpendicular reference plates. Each plate is covered by an adhesive white waterproof paper with four accurately printed fiducial markers (see Fig. 6(a) and 6(d)). These markers, with known distances between each other, help to define the position of each reference plate in the real world coordinates. As mentioned before, these markers, especially edges or corners of the patterns, are always too vague to be accurately detected in thermal images even after heating. It is well known that the printed black ink has higher emissivity than the white paper. But the emissivity difference between them is often small, so even though the black pattern absorbs more heat than the white paper when exposed to a heating lamp, the fast heat conduction soon leads to a smooth thermal distribution across pattern edges. One solution to this problem is taking the thermal image as soon as the heating starts, so that the heat conduction process almost does not have time to develop. This was achieved in this paper by imaging at 100 Hz while exposing the paper to an external flash. In this way, we could get sharp corners in the thermal image, as shown in Fig. 6(e). It is noted that the printed black ink appears bright while the white paper is black in the thermal image. For a sequence of experiments in which the setup remains the same, the calibration of the laser plane is only required for one time, because the motion of the Galvo scanner, the MIR laser, and the photographing of the IR camera were synchronized so that the position of the laser plane captured in every thermal image was consistent. The MIR laser was synchronized in terms of switching on at the beginning of each scan and switching off at the end.
Thermal images are processed with a method based on spatially and temporally analyzing the image sequence used in visible laser scanning [32]. Normally, two edges, the incoming edge and the leaving edge, of the laser line are detected by the method. However, it should be noted that instead of having a distinct line with two edges, only the incoming edge of the MIR laser line is clear while the leaving edge is not because heat in scanned region takes some time to dissipate. This is illustrated by Fig. 7(a) where an MIR laser line is scanning across two perpendicular reference plates from right to left. The incoming edge is much sharper than the leaving edge. To further understand this, the intensity distribution along the 100th row in the image is shown in Fig. 7(b). The intensity in thermal images, or the temperature on the plate’ surface, stays constantly low where the laser line has not swept, and climbs up sharply when the surface approaches the incoming edge of the line. The intensity reaches its peak at the center of the line (i.e. the center of laser radiation), and then drops first sharply but then gradually to a level that is higher than the original. As a result, only the incoming edge of the MIR laser line was analyzed in this paper.
With the geometric calibration information of the IR camera and the MIR laser plane, the 3-D points associated to corresponding image pixels of detected incoming edges of laser lines could be retrieved by intersecting laser sheets with camera rays. After that, a water-tight surface can be reconstructed from the 3-D points by the Poisson surface reconstruction method.
To verify the MIR laser line scanning method, the same glass bowl and ice bowl in Fig. 4(a) and 4(c) were measured in a cold environment with a temperature of −20 °C. During the scanning measurement, the freezer door was opened. The laser power and the image frequency were set to 4.5 W and 40 Hz, respectively. Every scan took around 23 s. Final reconstructed surfaces of the glass bowl and the ice bowl are shown in Fig. 8(a) and 8(b). Again, the reconstructed surfaces from MIR laser line scanning were compared to aforementioned visible laser scanning result. The difference between them is also measured in terms of the signed distance. It is clear that although the reconstructed surface of the glass bowl has a larger extreme deviation than the ice bowl surface, these large deviations occur only around the bowl rim. Within the bowl, the error of the glass bowl results is smaller and experiences less fluctuation. This can be further demonstrated by the error distribution in Fig. 8(c) and 8(d). Signed distances of ice bowl results span in a wider range, and the distribution has two peaks. The mean value and the standard deviation of the signed distance for glass bowl results are 0.023 mm and 0.21 mm, while these values for ice bowl results are −0.039 mm and 0.29 mm. Compared to point scanning results from last section in Fig. 5, generally, the line scanning results display higher accuracy and lower uncertainty.
Fig. 8 Comparison of MIR laser line scanning on glass bowl and ice bowl. (a) Glass bowl reconstructed surface and error. (b) Ice bowl reconstructed surface and error. (c) Error distribution of glass bowl results. (d) Error distribution of ice bowl results.
4.1 Line scanning on glass bowl and ice bowl
4.2 Line scanning on plastic frustum and ice frustum
To further validate the MIR laser line scanning method, a specially designed ice frustum is made that covers roughness features of aircraft icing. A digital frustum model is first designed in CAD software, and then printed into a plastic frustum through the 3-D printing technique. After that, a silicone mold is made from the plastic frustum. At last, an ice frustum can be casted by placing the silicone mold filled with water in a freezer. The separation of the ice frustum from the silicone rubber is very easy and the silicone rubber works very well with long-term stability even under low temperatures, so the designed shape is well preserved on each reproduction of the ice frustum. The plastic frustum and the corresponding ice frustum are shown in Fig. 9(a) and 9(b). The designed model is composed of a base plate and a matrix of identical frustums. Dimensions of the base plate are 100 × 52 × 5 mm (length, width, height). Each frustum has a height of 3 mm.
The MIR laser line scanning method was applied to measure the ice frustum shape. The parameters of the laser, camera, and galvo scanner were kept the same as before. To eliminate the occlusion and acquire a full representation of the model, three scans of differently positioned frustums were carried out. Each scan produced a 3-D point cloud of one part of the model. In the end, three point clouds were generated. To align these point clouds, a method based on the iterative closest point (ICP) algorithm [42] was used. Finally, a water-tight surface of the frustum was computed through the Poisson surface reconstruction. As a comparison, the measurement of the plastic frustum based on the visible laser scanning method is also presented here.
Final reconstructed surfaces of the plastic frustum and the ice frustum are shown in Fig. 10(a) and 10(b). Both results are evaluated with the true geometry of the model. Error distributions of both results are illustrated in Fig. 10(c) and 10(d). The mean error and standard deviation for the plastic frustum are 0.0029 mm and 0.18 mm. For the ice frustum, these two values are −0.0051 mm and 0.23 mm. Before a further comparison between results from two frustums, let us first look back at the results of the ice bowl in Fig. 8(b) and 8(d). Signed distances of the ice frustum results display less fluctuation and a narrower distribution than those of the ice bowl results, which proves the necessity of verifying the MIR laser line scanning method on a designed ice shape with a precisely known 3-D geometry. A comparison between Fig. 10(a) and 10(b) shows that MIR laser line scanning did not capture some details of frustums, especially the top circle plane. The reason for this problem is that the ability of the scanning method to detect tiny features is mostly limited by the image resolution, or, to be more precise, the pixel scale. For measurements of the plastic frustum, we used a visible light camera with a resolution of 1280 × 1024 pixels which is exactly four times the resolution of the IR camera. Higher image resolution means correspondingly a denser 3-D point cloud, which is also indicated by a larger area of the error distribution of visible laser scanning results; see Fig. 10(c) and 10(d). However, the test on the ice frustum concludes that despite of a limited image resolution, the MIR laser line scanning method is proved to be capable of measuring ice shapes with high accuracy. In addition, due to a higher image resolution, the traditional visible laser line scanning method is a good choice to evaluate the MIR method on the same object but with a diffuse reflective surface.
Fig. 10 Comparison of visible laser line scanning on plastic frustum and MIR laser line scanning on ice frustum. (a) Plastic frustum reconstructed surface and error. (b) Ice frustum reconstructed surface and error. (c) Error distribution of plastic frustum results. (d) Error distribution of ice frustum results.
4.3 Line scanning on ice accretions in the icing wind tunnel
Finally, the practicability of this MIR laser line scanning method in icing tunnel experiments was validated through measuring the shape evolution of ice accretions on the upper surface of a NACA 0012 airfoil in a multi-phase and icing wind tunnel. The icing wind tunnel, located at the Institute of Fluid Mechanics at Technische Universität Braunschweig, is a newly built closed loop wind tunnel; see Fig. 11. The test section has a length of 1.5 m and a cross section of 0.5 × 0.5 m. Free stream flow in the test section can reach a maximum speed of 40 m/s. The air temperature within the tunnel can be adjusted down to −20 °C. Artificial water droplets clouds are generated by a spray grid composed of 5 × 5 spray nozzles to simulate the icing process during the flight. At the time of presented work, many properties of this icing wind tunnel such as flow uniformity and turbulence, temperature distribution, mean droplet diameter, and cloud uniformity were still under calibration and certification. Therefore, the tunnel was not ready to reproduce the exact icing process that happens to aircrafts under natural atmospheric conditions. However, there was no problem for it to produce different ice types for the verification of a method developed to measure ice shapes.
In the experiments, the IR camera, the MIR laser, and the galvo scanner were mounted above the top window of the test section of the icing wind tunnel, as shown in Fig. 12(a). The MIR laser sheet was projected inside the test section through an anti-reflection coated germanium window which has a high transmittance (>97%) for the wavelength of 10.6 μm. A heat gun was placed near the germanium window to blow hot air flowing across the surface of the window during icing experiments. Otherwise, a water film would condensate on the germanium window, which, of course, would block the MIR laser sheet and may damage the window. A visible light camera was used to photograph visual images of ice shapes immediately following each scan. Optical access was realized through a traditional soda-lime double layer window. These traditional visual images serve as a qualitative comparison for MIR measurements. For the IR camera, as before, it observed the emission generated by the laser excitation through a sapphire window. The laser power, image frequency of the IR camera, and the scanning time were set to 4.5 W, 50 Hz, and 22 s, respectively. Before the installation of the airfoil, the IR camera and the laser plane were calibrated by the method mentioned in the beginning of this section. The two perpendicular reference plates were positioned close to where the leading edge of the airfoil would appear. The clean airfoil was scanned before and after wind on to compensate the mechanical distortion, if any, induced by the movement or the vibration of the airfoil. In experiments, no movement of the airfoil was observed. For icing process measurements, each ice shape was scanned only once at one view direction because the occlusion was not serious. One example of scanning images of ice is shown in Fig. 12(b). The IR camera captured an MIR laser line, starting from the leading edge along the flow direction, scanning spanwisely across the ice accretion on the upper surface of the airfoil. Again, it is demonstrated in Fig. 12(b) that only the incoming edge of the MIR laser line is identifiable, whereas the leaving edge is merged with radiation patterns of the scanned region behind the laser line.
The temperature of the air flow in the icing tunnel was set to around −5 °C. The freestream velocity was set to 40 m/s. Proper water flow rate and air pressure in spray nozzles were adjusted so that clear ice could be generated on the airfoil. The water was sprayed for 6 minutes. The ice accretion was scanned every 1 minute, thus 6 times in total. During each scan, the water spray was suspended to allow the camera have a more clear view. At the same time, the refrigeration of the air flow in the tunnel remained unchanged, which is necessary to maintain a stable low temperature in the tunnel. Because the low laser power was used, laser-irradiated heat on the ice surface dissipated very fast in the freezing air flow. When the water spray was switched on again after the scan, the influence of laser irradiation on the ice growth was neglectable.
The six final reconstructed surfaces of ice shapes at six time points, t1, t2, t3, t4, t5, and t6, are shown in Fig. 13. As a comparison, the corresponding visual images are also shown in Fig. 13. Because the IR camera and the visual camera looked at the icing surface from two different viewing angles (see Fig. 12(a)), there are some perspective differences between reconstructed surfaces and visual images, despite some adjustments of viewing directions of the results. In addition, translucent ice posed a problem for the visual camera to capture the ice surface, which explains often low contrast or unidentifiable ice features in visual images. Nonetheless, some gross ice features presented in these visual images still help to qualitatively evaluate the MIR laser line scanning results. For the icing process of clear ice, water droplets do not freeze immediately when they impact on the surface of an object. Instead, these water droplets run back and freeze afterwards. This explains why all
reconstructed surfaces and visual images capture a relatively smooth and simple appearance of ice near the leading edge of the airfoil while complicated ice features otherwise. At the very beginning of ice growth t1, run-back water droplets formed spanwise ridges, which are captured by the scanning result and are also identifiable in the visual image. As the time went on, these ridges were replaced by growing irregular ice bumps or feathers which are well captured by scanning results, and also indicated by visual images. The results in Fig. 13 show that the MIR laser line scanning method is a very promising method to trace the 3-D shape evolution of ice accretions in the icing research.
To quantitatively evaluate MIR laser line scanning results of ice accretions, the mold and casting method was used to replicate the final ice shape after wind tunnel experiments. The mold making silicone fluid and a specially designed wooden box for the molding had been stored in a freezer (−25 °C) before experiments. After all scanning measurements finished, the silicone fluid was first mixed with proper corresponding catalyst, and then poured into the mold box. The mixture was stored in the freezer for 30 minutes, to allow large air bubbles generated during mixing to float to the surface, before the iced airfoil was carefully inserted into it and fixed in the mold box. The low temperature of the freezer prohibited ice from melting during the whole process. At last, the mold box was transferred to another freezer with a higher temperature of −5 °C to reduce the cure time. The mixture could solidify over the night. The casting was finished next morning still inside the wooden box but at room temperature. The mixture of polyurethane liquid was poured in the wooden box. To save casting liquid, the clean airfoil was inserted into the mixture, leaving some gaps from the mold, and fixed in the box afterwards. The procedure of this mold and casting method to replicate the final ice shape on the airfoil is briefly illustrated in Fig. 14(a)-14(e).
Fig. 14 The procedure of mold and casting. (a) Airfoil fixed in the box. (b) Molding in the box. (c) Casting in the box. (d) Negative mold. (e) Replication of final ice shape.
As soon as the final ice shape was replicated by the casting, the visible laser line scanning method was applied to measure the casting shape. Overall 8 scans at different viewing angles of the central part of the casting were carried out. One example of the 8 viewing directions of the casting is shown in Fig. 15(a). As before, 8 point clouds were aligned by the ICP method according to overlapping scanning zones. In the end a water-tight surface of the central part of the casting was reconstructed; see Fig. 15(b). The MIR laser line scanning result of the final ice accretion (t6) in Fig. 13 was compared with the visual scanning result of the casting. The deviation map is shown in Fig. 15(c). The error distribution is given in Fig. 15(d). The mean signed distance is −0.036 mm and the standard deviation is 0.63 mm. It is clear that the two results have a perfect match except for several large deviations in the feather region. Two reasons are mainly responsible for these large deviations. First, because of the complicated geometry of ice feathers, some of them may get blocked by others in the view of either the IR camera or the MIR laser sheet, so they could not be measured by a single scan, and thus, are not present in the final MIR reconstruction. This accounts for the blue colored region in Fig. 15(c). Second, during the mold and casting, some fragile ice feathers may fall off, so they are missing in the final visual reconstruction. This accounts for the red colored region in Fig. 15(c). In addition, because the silicone fluid mixture was not degassed by a vacuum pump, some air bubbles retained in the interface between the ice accretion and the silicone fluid. That could also degrade the fidelity of the mold and the subsequent replication of ice. The shrinkage and warping of the mold and the casting were also reported to introduce some errors [9].
Fig. 15 Comparison of MIR ice scan and visual casting scan. (a) Image of casting. (b) Reconstructed surface of casting. (c) Deviation of MIR ice scan from visual casting scan. (d) Deviation distribution.
To further study the difference between MIR laser line scanning results of the ice accretion and visual scanning results of the casting, profiles at a cross section cut are shown in Fig. 16(a). Generally, a good agreement between the ice profile and the casting profile is observed, especially at the relatively smooth region near the leading edge. As it approaches the feather region, large deviations arise from causes mentioned above. However, this problem will be greatly alleviated in the future if, first, multiple MIR scans at different viewing angles are implemented, and second, fragile ice feathers are well preserved during the mold and casting.
The biggest advantage of MIR laser line scanning over traditional visible laser line scanning is that the requirement of spraying opaque dyestuff on the ice surface is not necessary any more. This helps to not only simplify the experimental process dramatically, but also avoid any possible damage of ice shapes when applying such a spray. And most of all, MIR scanning provides an efficient, effective, and real solution to trace the 3-D shape evolution of ice accretions in icing wind tunnels. Traditional methods tracing the shape of ice growth have to run the tunnel several times [10], because they cause severe interruption of the icing process. This will cost external financial, physical, and human resources. Worse more, there is no guarantee that the same ice shape forms during each wind tunnel run. The repeatability of ice shapes has only been well established for a given set of icing conditions [43]. And study shows that even small parameter variations might produce discernible ice feature changes [44]. For MIR scanning, all measurements tracing the ice growth can be done within a single wind tunnel run. Reconstructed ice surfaces in Fig. 13 have already demonstrated this enormous advantage of MIR scanning, but 2-D ice profiles at a cross section cut in Fig. 16(b) offer a more straightforward impression. In Fig. 16(b), the continuous growth of ice accretions on the airfoil, not only at the smooth region but also at the feather region, is illustrated.
5. Conclusions
Because the ice accretion on the surface of aircrafts is always a mixture of translucent clear ice and white rime ice, and sometimes transparent supercooled water droplets or films sporadically are involved as well, traditional methods to measure the shape of the ice accretion all suffer from certain defects. In this paper, a method based on mid-infrared (MIR) laser scanning was proposed to trace the 3-D shape evolution of the ice growth without any interruption in the icing process. A thorough analysis of radiative properties of clear ice, rime ice, and water showed that a scanning technique based on an MIR laser source at the wavelength of 10.6 μm is a general method to determine the shape of all three materials at the same time. This was proved by an MIR laser point scanning technique on an ice model. Because of the low efficiency and often sparse results of point scanning, an MIR laser line scanning technique was developed and validated. At last, the MIR laser line scanning technique was applied to recover the 3-D shape development of the continuous growth of ice, mostly clear ice, on the NACA 0012 airfoil in the icing wind tunnel. The temporal evolution of the ice shape was successfully observed in both the reconstructed 3-D ice surfaces and the 2-D ice profiles at a cross section cut. The MIR scanning result on the final ice accretion fits well to the visual scanning result on a plastic replication of the final ice made from the mold and casting method.
Future work includes the implementation of multiple scans on the iced airfoil by the MIR laser line scanning method and the combination of ice shape measurements and heat transfer coefficient measurements on the iced surface.
References and links
1. M. Bragg, A. Broeren, and L. Blumenthal, “Iced-airfoil aerodynamics,” Prog. Aerosp. Sci. 41(5), 323–362 (2005). [CrossRef]
2. H. Addy, D. Sheldon, and M. Potatpczuk, Jr., “Modern Airfoil ice accretions,” in 35th Aerospace Sciences Meeting and Exhibit, 97–0174 (American Institute of Aeronautics and Astronautics, 1997).
3. P. Collier, L. Dixon, D. Fontana, D. Payne, and A. W. Pearson, “The Use of Close Range Photogrammetry for Studying Ice Accretion on Aerofoil Sections,” Photogramm. Rec. 16(94), 671–684 (1999). [CrossRef]
4. R. J. Hansman Jr, M. S. Kirby, R. C. McKnight, and R. L. Humes, “In-flight measurement of airfoil icing using an array of ultrasonic transducers,” J. Aircr. 25(6), 531–537 (1988). [CrossRef]
5. C. R. Mercer, M. Vargas, and J. R. Oldenburg, “A preliminary study on ice shape tracing with a laser light sheet,” NASA Tech. Memo. 105964 (1993).
6. R. C. McKnight, R. L. Palko, and R. L. Humes, “In-flight photogrammetric measurement of wing ice accretions,” in 24th Aerospace Sciences Meeting, 86–0483 (American Institute of Aeronautics and Astronautics, 1986). [CrossRef]
7. E. Hovenac and M. Vargas, “A laser-based ice shape profilometer for use in icing wind tunnels,” NASA Tech. Memo, 106936 (1995).
8. Y. Han, J. L. Palacios, and E. C. Smith, “An Experimental Correlation between Rotor Test and Wind Tunnel Ice Shapes on NACA 0012 Airfoils,” in SAE 2011 International Conference on Aircraft and Engine Icing and Ground Deicing, 2011–38–0092 (Society of Automotive Engineers, 2011). [CrossRef]
9. S. Lee, A. P. Broeren, R. E. Kreeger, M. G. Potapczuk, and L. Utt, “Implementation and Validation of 3-D Ice Accretion Measurement Methodology,” in 6th AIAA Atmospheric and Space Environments Conference, 2014–2613 (American Institute of Aeronautics and Astronautics, 2014). [CrossRef]
10. S. T. McClain, D. Reed, M. M. Vargas, R. E. Kreeger, and J.-C. Tsao, “Ice Roughness in Short Duration SLD Icing Events,” in 6th AIAA Atmospheric and Space Environments Conference, 2014–2330 (American Institute of Aeronautics and Astronautics, 2014). [CrossRef]
11. R. E. Kreeger and J.-C. Tsao, “Ice Shapes on a Tail Rotor,” in 6th AIAA Atmospheric and Space Environments Conference, 2014–2612 (American Institute of Aeronautics and Astronautics, 2014). [CrossRef]
12. I. Ihrke, K. Kutulakos, and H. Lensch, “State of the art in transparent and specular object reconstruction,” in EUROGRAPHICS 2008 STAR (EUROGRAPHICS Association, 2008), pp. 87–108.
13. S. K. Lau, D. P. Almond, and J. M. Milne, “A quantitative analysis of pulsed video thermography,” NDT Int. 24(4), 195–202 (1991). [CrossRef]
14. E. Barker, “Shape reconstruction from a single thermal image,” Opt. Eng. 34(1), 154–159 (1995). [CrossRef]
15. G. Eren, O. Aubreton, F. Meriaudeau, L. A. Sanchez Secades, D. Fofi, A. T. Naskali, F. Truchetet, and A. Ercil, “Scanning from heating: 3D shape estimation of transparent objects from local surface heating,” Opt. Express 17(14), 11457–11468 (2009). [CrossRef] [PubMed]
16. F. Meriaudeau, L. Alonso Sanchez Secades, G. Eren, A. Ercil, F. Truchetet, O. Aubreton, and D. Fofi, “3-D Scanning of Nonopaque Objects by Means of Imaging Emitted Structured Infrared Patterns,” IEEE Trans. Instrum. Meas. 59(11), 2898–2906 (2010). [CrossRef]
17. A. Bajard, O. Aubreton, G. Eren, P. Sallamand, and F. Truchetet, “3D digitization of metallic specular surfaces using scanning from heating approach,” Proc. SPIE 7864, 786413 (2011). [CrossRef]
18. O. Aubreton, A. Bajard, B. Verney, and F. Truchetet, “Infrared system for 3D scanning of metallic surfaces,” Mach. Vis. Appl. 24(7), 1513–1524 (2013). [CrossRef]
19. A. Bajard, A. Olivier, B. Youssef, V. Benjamin, G. Eren, A. Erçil, and F. Truchetet, “Three-dimensional scanning of specular and diffuse metallic surfaces using an infrared technique,” Opt. Eng. 51(6), 063603 (2012). [CrossRef]
20. T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th ed. (John Wiley & Sons, 2011).
21. S. Warren, “Optical properties of snow,” Rev. Geophys. 20(1), 67–82 (1982). [CrossRef]
22. A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, “The ASTER spectral library version 2.0,” Remote Sens. Environ. 113(4), 711–715 (2009). [CrossRef]
23. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23(8), 1206–1224 (1984). [CrossRef] [PubMed]
24. G. M. Hale and M. R. Querry, “Optical Constants of Water in the 200-nm to 200- µm Wavelength Region,” Appl. Opt. 12(3), 555–563 (1973). [CrossRef] [PubMed]
25. H. D. Baehr and K. Stephan, Heat and Mass Transfer, 2nd ed. (Springer, 2006).
26. M. Hori, T. Aoki, T. Tanikawa, H. Motoyoshi, A. Hachikubo, K. Sugiura, T. J. Yasunari, H. Eide, R. Storvold, Y. Nakajima, and F. Takahashi, “In-situ measured spectral directional emissivity of snow and ice in the 8–14 μm atmospheric window,” Remote Sens. Environ. 100(4), 486–502 (2006). [CrossRef]
27. J. A. Sobrino and J. Cuenca, “Angular variation of thermal infrared emissivity for some natural surfaces from experimental measurements,” Appl. Opt. 38(18), 3931–3936 (1999). [CrossRef] [PubMed]
28. L. Gerhardt, “The use of laser structured light for 3D surface measurement and inspection,” in Proceedings of the Fourth International Conference on Computer Integrated Manufacturing and Automation Technology (IEEE, 1994), pp. 215–221.
29. F. S. Marzani, Y. Voisin, L. F. C. L. Y. Voon, and A. Diou, “Calibration of a three-dimensional reconstruction system using a structured light source,” Opt. Eng. 41(2), 484–492 (2002).
30. M. Kazhdan, M. Bolitho, and H. Hoppe, “Poisson Surface Reconstruction,” in Proceedings of the Fourth Eurographics Symposium on Geometry Processing (Eurographics Association, 2006), pp. 61–70.
31. F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13(1), 231–243 (2004). [CrossRef]
32. D. Lanman and G. Taubin, “Build Your Own 3D Scanner: 3D Photography for Beginners,” in ACM SIGGRAPH 2009 Courses (ACM, 2009), pp. 8:1–8:94.
33. S. Y. Cheng, S. Park, and M. M. Trivedi, “Multiperspective Thermal IR and Video Arrays for 3D Body Tracking and Driver Activity Analysis,” in Computer Vision and Pattern Recognition-Workshops,2005. CVPR Workshops (IEEE, 2005), Vol. 3, pp. 1–8.
34. S. Vidas, R. Lakemond, S. Denman, C. Fookes, S. Sridharan, and T. Wark, “A Mask-Based Approach for the Geometric Calibration of Thermal-Infrared Cameras,” IEEE Trans. Instrum. Meas. 61(6), 1625–1635 (2012). [CrossRef]
35. P. Engström, H. Larsson, and J. Rydell, “Geometric calibration of thermal cameras,” Proc. SPIE 8897, 88970C (2013). [CrossRef]
36. Y. H. Ng and R. Du, “Acquisition of 3D surface temperature distribution of a car body,” in 2005 IEEE International Conference on Information Acquisition (IEEE, 2005), pp. 16–20. [CrossRef]
37. G. Cardone, A. Ianiro, G. dello Ioio, and A. Passaro, “Temperature maps measurements on 3D surfaces with infrared thermography,” Exp. Fluids 52(2), 375–385 (2011). [CrossRef]
38. V. Hilsenstein, “Surface reconstruction of water waves using thermographic stereo imaging,” presented at Image and Vision Computing New Zealand 2005, Dunedin, New Zealand, 102–107 Nov. 2005.
39. J.-Y. Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/index.html.
40. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000). [CrossRef]
41. Josep Forest i Collado, “New methods for triangulation-based shape acquisition using laser scanners,” PhD thesis, University of Girona (1997).
42. P. J. Besl and H. D. McKay, “A Method for Registration of 3-D Shapes,” IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 239–256 (1992). [CrossRef]
43. S. Jaiwon and H. Thomas, “Repeatability of Ice Shapes in the NASA Lewis Icing Research,” J. Aircr. 31(5), 1057–1063 (1994). [CrossRef]
44. D. Miller, M. Potapczuk, and T. Langhals, “Preliminary Investigation of Ice Shape Sensitivity to Parameter Variations,” in 43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005–0073 (American Institute of Aeronautics and Astronautics, 2005). [CrossRef]
